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Mat. Sb., 1998, Volume 189, Number 10, Pages 53–74 (Mi msb350)  

This article is cited in 13 scientific papers (total in 13 papers)

Asymptotic and Fredholm representations of discrete groups

V. M. Manuilov, A. S. Mishchenko

M. V. Lomonosov Moscow State University

Abstract: A $C^*$-algebra servicing the theory of asymptotic representations and its embedding into the Calkin algebra that induces an isomorphism of $K_1$-groups is constructed. As a consequence, it is shown that all vector bundles over the classifying space $B\pi$ that can be obtained by means of asymptotic representations of a discrete group $\pi$ can also be obtained by means of representations of the group $\pi \times {\mathbb Z}$ into the Calkin algebra. A generalization of the concept of Fredholm representation is also suggested, and it is shown that an asymptotic representation can be regarded as an asymptotic Fredholm representation.

DOI: https://doi.org/10.4213/sm350

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English version:
Sbornik: Mathematics, 1998, 189:10, 1485–1504

Bibliographic databases:

UDC: 517.98
MSC: Primary 20C99, 46L99; Secondary 46L89, 55P91
Received: 06.03.1998

Citation: V. M. Manuilov, A. S. Mishchenko, “Asymptotic and Fredholm representations of discrete groups”, Mat. Sb., 189:10 (1998), 53–74; Sb. Math., 189:10 (1998), 1485–1504

Citation in format AMSBIB
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\paper Asymptotic and Fredholm representations of discrete groups
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Manuilov, “Almost-representations and asymptotic representations of discrete groups”, Izv. Math., 63:5 (1999), 995–1014  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. M. Manuilov, “On $C^*$-algebras related to asymptotic homomorphisms”, Math. Notes, 68:3 (2000), 326–332  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. S. Mishchenko, “A Theory of Almost Algebraic Poincaré Complexes”, Proc. Steklov Inst. Math., 231 (2000), 281–307  mathnet  mathscinet  zmath
    4. Manuilov, VM, “Quasidiagonal extensions and sequentially trivial asymptotic homomorphisms”, Advances in Mathematics, 154:2 (2000), 258  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. V. M. Manuilov, K. Thomsen, “The Connes–Higson map is an isomorphism”, Russian Math. Surveys, 56:4 (2001), 756–757  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. V. M. Manuilov, “On Asymptotic Homomorphisms into Calkin Algebras”, Funct. Anal. Appl., 35:2 (2001), 148–150  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Mishchenko, AS, “Theory of almost algebraic Poincaré complexes and local combinatorial Hirzebruch formula”, Acta Applicandae Mathematicae, 68:1–3 (2001), 5  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Manuilov, VM, “Almost, asymptotic and Fredholm representations of discrete groups”, Acta Applicandae Mathematicae, 68:1–3 (2001), 159  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    9. Manuilov V.M., “Asymptotic homomorphisms into the Calkin algebra”, J. Reine Angew. Math., 557 (2003), 159–172  crossref  mathscinet  zmath  isi  elib
    10. Manuilov, V, “The Connes-Higson construction is an isomorphism”, Journal of Functional Analysis, 213:1 (2004), 154  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    11. A. I. Shtern, “Kazhdan–Milman problem for semisimple compact Lie groups”, Russian Math. Surveys, 62:1 (2007), 113–174  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. A. I. Shtern, “Finite-dimensional quasirepresentations of connected Lie groups and Mishchenko's conjecture”, J. Math. Sci., 159:5 (2009), 653–751  mathnet  crossref  mathscinet  zmath  elib  elib
    13. Shtern I A., “Continuity Conditions For Finite-Dimensional Locally Bounded Representations of Connected Locally Compact Groups”, Russ. J. Math. Phys., 25:3 (2018), 345–382  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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